Multiconfiguration Self-Consistent-Field Wave Functions

Derivatives from Multiconfiguration Self-Consistent-Field Wave Functions 

We assume that an MCSCF calculation has been carried out at the reference geometry X0 and denote the MCSCF state at this geometry by MC . The MCSCF state may be expressed as 

The total energy of the MCSCF state at the displaced geometry is 

Inserting the Hamiltonian expansion [Eq. (27)] in Eq. (52) and using the BCH expansion, we obtain 

The geometry dependence of the variational parameters A is determined from the requirement that the total energy in Eq. (55) must be stationary in the perturbed field  

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Olsen J and J0rgensen P 1995 Time-dependent response theory with applications to self-consistent field and multiconfigurational self-consistent field wave functions Modern Electronic Structure Theory vo 2, ed D R Yarkony (Singapore World Scientific) pp 857-990... 

J. Olsen and P. Jorgensen. Time-Dependent Response Theory with Applications to Self-Consistent Field and Multiconfigurational Self-Consistent Field Wave Functions, in Modern Electronic Structure Theory, edited by D. R. Yarkony, volume 2, chapter 13, pp. 857-990. World Scientific, Singapore, 1995. 

Calculation of rotational and vibrational g factors by linear response methods using multiconfigurational self-consistent-field wave functions is described in detail elsewhere [18,27]. 

III. Derivatives from Multiconfiguration Self-Consistent-Field Wave Functions... 

P. Jprgensen, H. Jensen, J. Olsen, Linear response calculations for large scale multiconfiguration self-consistent field wave functions, J. Chem. Phys. 89 (1988) 3654-3661. 

P. Pulay, J. Chem. Phys., 78, 5043 (1983). Second and Third Derivatives of Variational Energy Expressions Application to Multiconfigurational Self-Consistent Field Wave Functions. 

It is possible to divide electron correlation as dynamic and nondynamic correlations. Dynamic correlation is associated with instant correlation between electrons occupying the same spatial orbitals and the nondynamic correlation is associated with the electrons avoiding each other by occupying different spatial orbitals. Thus, the ground state electronic wave function cannot be described with a single Slater determinant (Figure 3.3) and multiconfiguration self-consistent field (MCSCF) procedures are necessary to include dynamic electron correlation. 

Another class of methods uses more than one Slater determinant as the reference wave function. The methods used to describe electron correlation within these calculations are similar in some ways to the methods listed above. These methods include multiconfigurational self-consistent field (MCSCF), multireference single and double configuration interaction (MRDCI), and /V-clcctron valence state perturbation theory (NEVPT) methods.5... 

Pioneering theoretical work on the formaldehyde -I- OH reaction has been reported by Dupuis and Lester [102] using multiconfiguration self-consistent-field (MCSCF) and configuration interaction (Cl) wave functions. These authors [102] predicted a large positive activation barrier of 5.5 kcal/mol. Using the ab initio Moller-Plesset method up to fourth order (MP4), Francisco [103] determine the barriers and energetic of this reaction. He obtained a small but positive barrier of... 

Olsen, J., lorgcnsen, P. Time dependent response theory with appUcations in to self consistence field (SCF and multiconfigurational self consistent field (MCSCF) wave functions, l.F.A. PRINT, Aarhus Universitet, 1994... 

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